Journal of Optics B Quantum and Semiclassical Optics

Spectrum and eigenstates for a model describing optical second harmonic generation

Ying Wu, Xiaoxue Yang

Published Sep 15, 2003• 6 citations

Abstract

Without using the assumption of the Bethe ansatz, we have obtained exact explicit analytical expressions for the energy spectrum and eigenstates in terms of a parameter λ for a model of optical second harmonic generation. We have shown that the parameter λ is determined by the roots of a polynomial of order [( N +1)/4]. Here [ y ] denotes y ' s integer part and N = n a +2 n b with n a and n b being photon numbers of the fundamental and the second harmonic modes respectively. We also obtain explicit analytical expressions for λ for , and explicit analytical expressions for all the eigenstates without showing any interactions between the two modes.

DOI: 10.1088/1464-4266/5/5/007

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